ixteen years ago, on a cold February day at Yale University, a poster caught Gil Kalai’s eye. It advertised a series of lectures by Michel Devoret, a well-known expert on experimental efforts in quantum computing. The talks promised to explore the question “Quantum Computer: Miracle or Mirage?” Kalai expected a vigorous discussion of the pros and cons of quantum computing. Instead, he recalled, “the skeptical direction was a little bit neglected.” He set out to explore that skeptical view himself.

Today, Kalai, a mathematician at Hebrew University in Jerusalem, is one of the most prominent of a loose group ...